Exploring different explainable artificial intelligence algorithms applied to a LSTM for streamflow modelling

Machine Learning and Deep Learning have been proving their potential for streamflow modelling in various studies. In particular, long short-term memory (LSTM) models showed exceptionally good results. However, machine learning models often are considered “black boxes” with limited interpretability. Explainable artificial intelligence (XAI) comprise methods that analyze the internal processes of the machine learning network and allow to have a glance in the “black box”. Most proposed XAI techniques are designed for the analysis of images, and there is currently only limited work on time series data available.

In our study, we applied various XAI algorithms including gradient-based methods (Saliency, InputXGradient, Integrated Gradient, GradientSHAP) but also perturbation-based methods (Feature Ablation, Feature Permutation) to compare their applicability for reasonable interpretation in the hydrological context. To our knowledge, only Integrated Gradient has been applied to a LSTM in hydrology so far. Gradient-based methods analyze the gradient of the output with respect to the input feature. Whereas perturbation-based methods gain information by altering or masking specific input features. The different methods were applied to a LSTM trained for the low-land Ems catchment in Germany, which has a major baseflow share of total streamflow.

We analyzed the results regarding their “timestep of influence”, which describes the amount of past days having importance for the prediction of streamflow at a particular day. All of the algorithms applied result in a comparable annual pattern, characterized by relatively small timesteps of influence in spring (wet season) and increasing timesteps of influence in summer and autumn (dry season). However, the range of the absolute days of attribution varies between the methods. In conclusion, all methods produces reasonable results and appear to be suitable for interpretation purposes.

Furthermore, we compare the results to ERA-5 reanalysis data and gained evidence that the LSTM recognizes soil water storage as the main driver for streamflow generation in the catchment: we found an inverse seasonality of soil moisture and timestep of influence.